H ∞ control of networked control systems based on event-time-driven model

This article considers the H _∞ control problem for a class of networked control systems (NCSs) based on the event-time-driven model, under which the considered NCS can be changed into a class of switched delay systems including an unstable subsystem. The Lyapunov functional exponential estimation method is adopted to solve the problem of H _∞ control for such systems. The switching controller is designed to make the considered system exponentially stable with an H _∞ norm bound in terms of linear matrix inequalities. The obtained results are less conservative than existing ones. Finally, one example is given to illustrate the effectiveness and benefit of the proposed method.     

H∞ output tracking fuzzy control for nonlinear systems with time-varying delay

This paper proposes an observer-based output tracking control via virtual desired reference model for a class of nonlinear systems with time-varying delay and disturbance. First, the Takagi–Sugeno fuzzy model represents the nonlinear system with time-varying delay and disturbance. Then we design an observer to estimate immeasurable states and controller to drive the error between estimated state and virtual desired variables (VDVs) to zero such that the overall control output tracking system has H_∞ control performance. Using Lyapunov–Krasovskii functional, we derive sufficient conditions for stability. The advantages of the proposed output control system are (i) systematic approach to derive VDVs for controller design; (ii) relaxes need for real reference model; (iii) drops need for information of equilibrium; (iv) relaxed condition is provided via three-step procedure to find observer and controller gain. We carry out simulation using a continuous stirred tank reactor system where the effectiveness of the proposed controller is demonstrated by satisfactory numerical results.     

H∞ control of nonlinear continuous-time systems based on dynamical fuzzy models

This paper presents a solution of the H_∞ control problem for a class of continuous-time nonlinear systems. The method is based on a fuzzy dynamical model of the nonlinear system. A suitable piecewise differentiate quadratic (PDQ) Lyapunov function is used to establish asymptotic stability of the closed-loop system. Furthermore, a constructive algorithm is developed to obtain the stabilizing feedback control law. The controller design algorithm involves solving a set of suitable algebraic Riccati equations. An example is given to illustrate the application of the method     

Adaptive output feedback control for nonlinear time-delay systems using neural network

This paper extends the adaptive neural network （NN） control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay, Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on Lyapunov- Krasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved, The feasibility is investigated by two illustrative simulation examples.     

Robust H ∞ control of uncertain nonlinear switched systems using constructive method

This paper focuses on the problem of robust H _?? control of nonlinear switched systems with parameter uncertainty via the multiple Lyapunov functions (MLFs) approach. The uncertain parameters are assumed to be in a known compact set and are allowed to enter the system nonlinearly. Based on the explicit construction of Lyapunov functions, which avoids solving the Hamilton-Jacobi-Isaacs (HJI) inequalities, sufficient conditions for the solvability of the robust H _?? control problem of cascade nonlinear switched systems are derived under some switching signal. Then, the result is extended to solve the robust H _?? control problem of nonlinear switched systems in strict feedback form. Finally, the effectiveness of the proposed results is illustrated through a simulation example.     

Robust sampled-data H ∞ output tracking control for a class of nonlinear networked systems with stochastic sampling

In this article, the problem of robust sampled-data H _∞ output tracking control is investigated for a class of nonlinear networked systems with stochastic sampling and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and can be extended to the case with multiple stochastic sampling periods. By the way of an input delay, the probabilistic system is transformed into a stochastic continuous time-delay system. A new linear matrix inequality-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H _∞. Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H _∞ output tracking design.     

Adaptive H2/H∞ tracking control for a class of uncertain robotic systems

This paper addresses the problem of designing mixed H₂/H_∞ tracking control for a large class of uncertain robotic systems. Nonlinear H_∞ control theory, H₂ control theory and intelligent adaptive control algorithm are combined to construct a hybrid adaptive/robust H₂/H_∞ tracking control scheme. One adaptive neural network system is constructed to approximate the behaviour of uncertain robot dynamics, and the other adaptive control algorithm is designed to estimate the behaviour of the modelled disturbance. Moreover, a robust H_∞ control algorithm is designed to attenuate the effects of the unmodelled disturbance. Only a set of algebraic matrix Riccati-like equations is required to implement the proposed mixed H₂/H_∞ tracking controller, and so an explicit and closed-form solution is obtained. Consequently, the mixed H₂/H_∞ adaptive/robust tracking controller developed here can be analytically computed and easily implemented. Finally, simulations are presented to illustrate the effectiveness of the proposed control algorithm.     

Non-fragile robust finite-time H ∞ control for nonlinear stochastic it? systems using neural network

This paper deals with the problem of non-fragile robust finite-time H _?? control for a class of uncertain nonlinear stochastic It? systems via neural network. First, applying multi-layer feedback neural networks, the nonlinearity is approximated by linear differential inclusion (LDI) under statespace representation. Then, a sufficient condition is proposed for the existence of non-fragile state feedback finite-time H _?? controller in terms of matrix inequalities. Furthermore, the problem of nonfragile robust finite-time H _?? control is reduced to the optimization problem involving linear matrix inequalities (LMIs), and the detailed solving algorithm is given for the restricted LMIs. Finally, an example is given to illustrate the effectiveness of the proposed method.     

Reliable observer-based H∞ control of uncertain state-delayed systems

This paper is concerned with the reliable H_∞ control design problem for linear state-delayed system using observed-based output feedback. It proposes a reliable control design scheme for the case of possibly a simultaneous presence of actuator failures and sensor failures. Modified algebraic Riccati inequalities are developed to solve the problem addressed. Based on this approach, observer-based feedback control laws are designed that guarantee closed-loop asymptotic stability and reduction of the effect of an augmented disturbance input on the controlled output of a prescribed level, not only when the system is operating properly, but also under actuator and sensor failures. A numerical example is presented to demonstrate the applicability and effectiveness of the proposed approach.     

Neural network solution for finite-horizon H ∞ state feedback control of nonlinear systems

In this article, neural networks are used to approximately solve the finite-horizon optimal H _∞ state feedback control problem. The method is based on solving a related Hamilton–Jacobi–Isaacs equation of the corresponding finite-horizon zero-sum game. The neural network approximates the corresponding game value function on a certain domain of the state-space and results in a control computed as the output of a neural network. It is shown that the neural network approximation converges uniformly to the game-value function and the resulting controller provides closed-loop stability and bounded L ₂ gain. The result is a nearly exact H _∞ feedback controller with time-varying coefficients that is solved a priori offline. The results of this article are applied to the rotational/translational actuator benchmark nonlinear control problem.     

H∞ Adaptive tracking control for switched systems based on an average dwell-time method

This paper investigates the H_∞ state tracking model reference adaptive control (MRAC) problem for a class of switched systems using an average dwell-time method. First, a stability criterion is established for a switched reference model. Then, an adaptive controller is designed and the state tracking control problem is converted into the stability analysis. The global practical stability of the error switched system can be guaranteed under a class of switching signals characterised by an average dwell time. Consequently, sufficient conditions for the solvability of the H_∞ state tracking MRAC problem are derived. An example of highly manoeuvrable aircraft technology vehicle is given to demonstrate the feasibility and effectiveness of the proposed design method.     

Design of finite-time H∞ controller for uncertain nonlinear systems and its application

This paper studies the problem of finite-time H _∞ control for strict feedback nonlinear systems with external disturbance. The finite-time stability theory, H _∞ control method, backstepping technique, together with adding a power integrator tool are combined to design a finite-time H _∞ state feedback controller. The obtained controller can make the closed-loop system finite-time convergent, and the influence of the external disturbance is attenuated to a given degree. Two numerical examples are presented to show the effectiveness and feasibility of the proposed method. Meanwhile, the proposed method is also applied to robot manipulators.     

Robust H ∞ model predictive control for uncertain systems using relaxation matrices

In this paper, a robust H _∞ model predictive control (MPC) technique is proposed for time-varying uncertain discrete-time systems in the presence of input constraints and disturbances. We formulate a minimization problem of the upper bound of finite horizon cost function subject to the terminal inequality for an induced l ₂-norm bound. In order to improve system performance, we propose an LMI condition for the terminal inequality by using relaxation matrices. The LMI condition guarantees induced l ₂-norm bounds of the system despite system uncertainty and disturbance. A numerical example shows the effectiveness of the proposed method.     

Robust H ∞ model reference tracking control for networked control systems with communication constraints

This paper studies the problem of H _∞ model reference tracking control for continuous time networked control systems (NCSs) with communication constraints. By using the continuous Jensen inequality, linear matrix inequality (LMI)-based H _∞ model reference tracking controller design for nominal NCSs with controller-to-actuator communication constraints is presented, and a new method is proposed to design H _∞ model reference tracking controllers for NCSs with both controller-toactuator and sensor-to-controller communication constraints. The results are also extended to NCSs with norm-bounded parameter uncertainties. The merits of the proposed methods lie in their less computational complexity and less conservatism, which are achieved by adopting continuous Jensen inequality and proposing new controller design methods, respectively. The simulation results illustrate the effectiveness of the proposed H _∞ model reference tracking controller design for NCSs with communication constraints.     

A new approach to robust reliable H∞ control for uncertain nonlinear systems

This paper focuses on the optimal robust reliable H_∞ control for a class of uncertain nonlinear systems with actuator faults. A new method of annihilating uncertain matrix is proposed. Based on this approach, a new method of disposing of the phenomenon of uncertain matrices multiplication is provided. In accordance with the method, the optimal robust reliable H_∞ control problem for uncertain nonlinear systems is settled by employing state feedback, in terms of linear matrix inequality (LMI). Finally, two illustrative examples are given to show the feasibility and validity of the proposed method.     

Robust H∞ containment control for uncertain multi-agent systems with inherent nonlinear dynamics

This article considers the distributed containment control problem of nonlinear multi-agent systems subject to parameter uncertainties and external disturbances. An appropriate controlled output function is defined to quantitatively analyse the effect of external disturbances on the containment control problem. By employing robust H_∞ control approach, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that all followers asymptotically converge to the convex hull spanned by the leaders with the prescribed H_∞ performance under fixed topology. Moreover, the unknown feedback matrix of the proposed protocol is determined by solving only two LMIs with the same dimensions as a single agent. Finally, a numerical example is provided to demonstrate the effectiveness of our theoretical results.     

Passivity and H∞ control of switched discrete-time nonlinear systems using linearisation

Local passivity and H_∞ control of switched discrete-time nonlinear systems are studied using the linearisation technique in this paper. We first establish LMI-based sufficient conditions under which theconsidered system is locally strictly QSR-dissipative. Then, two special cases of QSR-dissipativity, local passivity and l₂ gain, are investigated. In view of the derived conditions being all convex in linearised system matrices, local feedback passification and H_∞ control problems of switched discrete-time nonlinear systems are solved. The efficiency of the proposed method is verified through numerical examples.